An alpha particle can be produced in certain radioactive decays of nuclei and co

Question

An alpha particle can be produced in certain radioactive decays of nuclei and consists of two protons and two neutrons. The particle has a charge of q = +2e and a mass of 4.00 u, where u is the atomic mass unit, with 1 u = 1.661 1027 kg. Suppose an alpha particle travels in a circular path of radius 4.60 cm in a uniform magnetic field with B = 1.40 T. Calculate the following values.

(a) its speed
m/s

(b) its period of revolution
s

(c) its kinetic energy
eV

(d) the potential difference through which it would have to be accelerated to achieve this energy
V

Explanation / Answer

In magnetic field

magnetic force = centripetal force

q*v*B = m*v^2/r

v = qBr/m

q = + 2e = 2*1.6*10^-19 C

B = 1.4 T

r = radius = 0.046 m

m = 4u = 4*1.661*10^-27

speed v = 2*1.6*10^-19*1.4*0.046/(4*1.661*10^-27)

v = 3.1*10^6 m/s <<<<============ANSWER

====================

(b)

period of revolution T = 2*pi*r/v = 2*pi*0.046/(3.1*10^6)

T = 9.32*10^-8 s

-------------------

(c)

kinetic energy KE = (1/2)*m*v^2

KE = (1/2)*4*1.661*10^-27*(3.1*10^6)^2

KE = 3.19*10^-14 J

1 J = 1/(1.6*10^-19) eV

KE = 3.19*10^-14/(1.6*10^-19)

KE = 199375 eV

==============

(d)

KE = dV*q

potential difference dV = KE/q = 199375/2 = 99687.5 V

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